After the discovery of neutrino oscillations, the search for the 0νββ-decay became one of the most fundamental problems of neutrino physics. In this contribution the recent developments in the field of nuclear double beta decay are reviewed. The light Majorana neutrino mass mechanism of the neutrinoless double beta decay (0νββ-decay) is discussed in the context of recent neutrino oscillation data. The expected half-lives of the 0νββ-decay are calculated by assuming the normal and inverted hierarchy of neutrino masses. The problem of reliable determination of the 0νββ-decay nuclear matrix elements is addressed. A sterile neutrino νh contribution to the 0νββ-decay is investigated. From the lower bound on the 0νββ-decay half-life stringent constraints on the νh?νe mixing in a wide region of sterile neutrino masses are derived.
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